I have a D5100 with a Sigma 50-200 but I also have a a 2x and 3x teleconverter lens. The problem is that the teleconverters are screw on. Is there an adapter for this?
There are some details that will make it easier to answer your question. For example, are the 2x and 3x teleconverter lens made by Sigma or Nikon? Are they mounted on the front of the lens or between the lens and camera?
At any rate, as per Nikon you should only use adapters of the same brands: Sigma tele converters with Sigma lenses and Nikon tele converters with Nikkor lenses. But this is ONLY a recommendation and depends on the type of adapter. In the end if the adapter is rear mounted (i.e. mounted between the camera and the lens) the camera mount is what determines compatibility. Mechanically, most Nikon converters will typically mount between the camera and the lens and only support Nikon-mount lenses (F-mount for Nikon DSLRs or Z-mount for Nikon Mirrorless Cameras)-- There are Nikon screw-on adapters for the front of the lens but they are used on specific camera models, typically simpler point and shoot cameras.
On the other hand, Sigma says this two about specific tele converters "Usable Lenses and Combinations: SIGMA TELE CONVERTER TC-1401 and TC-2001 are dedicated to Tele Converter lenses, which should be used with only listed lenses. The converter cannot be attached to the camera and lens whose mount is different. Do not use the SIGMA TELE CONVERTER on top of another SIGMA TELE CONVERTER, or any other kinds of converters."
I found the Sigma info above at this link Sigma lens compatibility